Simulation on YouTube graph • Comparison with random choice of prices • Additional enhancement – locally improving pricing decisions Pricing Strategies for Viral Marketing on Social Networks David Arthur 1 , Rajeev Motwani 1 , Aneesh Sharma 2 , Ying Xu 1 1 Department of Computer Science , Stanford University 2 Institute for Computational and Mathematical Engineering, Stanford University Motivation Social Network Monetization • Current monetization model: • Advertising • Leaves huge gap between potential and current revenue • Facebook: • 2007 valuation – $15 billion • 2008 revenue (estimated) – $300 million • Proposed scheme: • Sell products through personal recommendations • Incentivize users to participate using cashback • Leverages network structure through trust on friends! Viral Marketing Results The paper is available for download from http://arxiv.org/abs/0902.3485 Contact Us: {darthur,rajeev,aneeshs,xuying}@cs.stanford.edu Model • Seller marketing a product on a social network • Each new buyer: • recommends the product to her friends • is promised a cashback for each friend that purchases the product • Seller chooses price for each recommendation • Each receiver: • buys the product with probability as a function of price • is more likely to buy a product if more friends recommend it Problem Objective • Find seller strategies that optimize expected revenue • Seller strategy – choose prices for potential buyers • Why expected? – people buy probabilistically • Assume that we start with a single initial buyer (seed) Seller Strategies • Two types of strategies are possible: • Adaptive: choice of price for a receiver depends on history of choices • Non-adaptive: prices are fixed before the process even starts! • Theorem: Finding optimal non-adaptive seller strategies is NP-hard. • Adaptive strategies can be strictly better, but computational hardness unknown 0 500 1000 1500 2000 2500 3000 1 2 3 4 5 6 7 8 9 10 11 Revenue Local search iterations Max Leaf Strategy Random strategy Theoretical Guarantee • Theorem: E[revenue of Max-Leaf] ≥ c × E[revenue of optimal strategy] For some positive constant c < 1, where c depends on the probability model. This guarantee holds for very general probability functions. Proof Sketch 1. Reduce social network to a graph with minimum degree 3 • Need to ensure revenue from degree 1 and 2 nodes is constant 2. Find a max-leaf spanning tree on this reduced graph • This graph has a linear number of leaves 3. Optimal strategy can have at most linear revenue Conclusions Algorithm • Max-Leaf strategy: • Find the Maximum Leaf Spanning Tree for the network, rooted at seed • Give the product to the interior nodes for free • Charge some (optimal) price from the leaves Sample Scenario $2 $7 $5 $0.5 • Adaptive strategies do not offer a big advantage • Simple influence-and-exploit non-adaptive strategies work well • Trying to improve solution through local search may be beneficial in practice Open Questions • Incorporating cost of sending recommendations (spamming friends) • What if buyers are non-myopic? • Can we implement this on Facebook/Orkut?